Question

Silver sulfadiazine burn-treating cream creates a barrier against bacterial invasion and releases antimicrobial agents directly into the wound. If 25.0 \(\mathrm{g} \mathrm{Ag}_{2} \mathrm{O}\) is reacted with 50.0 \(\mathrm{g} \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}\) what mass of silver sulfadiazine, \(\mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{N}_{4} \mathrm{SO}_{2},\) can be produced, assuming 100\(\%\) yield? $$ \mathrm{Ag}_{2} \mathrm{O}(s)+2 \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}(s) \longrightarrow 2 \mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{N}_{4} \mathrm{SO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

The mass of silver sulfadiazine that can be produced, assuming a 100% yield, is \(35.67 \thinspace g\).

Step-by-step solution

Find the molar mass of each compound

First, we need to find the molar mass of each compound involved in the reaction. Look up the atomic masses of the individual elements and multiply them by the number of atoms in the formula. Then add all of the results together to get the molar mass for each compound. Ag₂O: (2 * 107.868) + (1 * 16.00) = 231.736 g/mol C₁₀H₁₀N₄SO₂: (10 * 12.01) + (10 * 1.008) + (4 * 14.007) + (1 * 32.07) + (2 * 16.00) = 250.293 g/mol AgC₁₀H₉N₄SO₂: (1 * 107.868) + (10 * 12.01) + (9 * 1.008) + (4 * 14.007) + (1 * 32.07) + (1 * 16.00) = 357.144 g/mol

Convert the mass of each reactant to moles

Using the molar mass, we can convert the mass of each reactant to moles. For Ag₂O: \( moles = \frac{mass}{molar \thinspace mass} = \frac{25.0 \thinspace g}{231.736 \thinspace g/mol} = 0.1079 \thinspace mol \) For C₁₀H₁₀N₄SO₂: \( moles = \frac{50.0 \thinspace g}{250.293 \thinspace g/mol} = 0.1997 \thinspace mol \)

Determine the limiting reactant and theoretical yield

Use stoichiometry to calculate the theoretical yield for both reactants. Divide the number of moles of each reactant by the stoichiometric coefficient (the numbers that balance the chemical equation). For Ag₂O (using stoichiometric coefficient of 1): \(0.1079 \thinspace mol\) For C₁₀H₁₀N₄SO₂ (using stoichiometric coefficient of 2): \( \frac{0.1997 \thinspace mol}{2} = 0.09985 \thinspace mol \) The limiting reactant is the one that produces the least amount of product, so in this case, it's C₁₀H₁₀N₄SO₂.

Calculate the mass of the product, silver sulfadiazine

Since we found that C₁₀H₁₀N₄SO₂ is the limiting reactant, we will use it to calculate the mass of silver sulfadiazine that can be produced. From the balanced equation, we see that 2 moles of C₁₀H₁₀N₄SO₂ react to produce 2 moles of AgC₁₀H₉N₄SO₂. So the moles of product will be the same as the moles of the limiting reactant: \( 0.09985 \thinspace mol \). Now, we will convert the moles of product to mass: \( mass \thinspace of \thinspace product = moles \thinspace of \thinspace product \times molar \thinspace mass \) \( mass \thinspace of \thinspace AgC_{10}H_{9}N_{4}SO_{2} = 0.09985 \thinspace mol \times 357.144 \thinspace g/mol = 35.67 \thinspace g \) The mass of silver sulfadiazine that can be produced, assuming a 100% yield, is 35.67 g.

Key concepts

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that will be completely consumed first. It determines the maximum amount of product that can be formed. When two or more reactants are involved, they often combine in different proportions. To identify the limiting reactant, it's necessary to compare the mole ratio of reactants to the coefficients in the balanced chemical equation.

• Convert the mass of each reactant to moles using their respective molar masses.
• Use the stoichiometric ratios from the balanced equation to calculate the theoretical moles of product each reactant can produce.
• The reactant that forms the lesser amount of product is the limiting reactant.

In our example, we've determined that \(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}\) is the limiting reactant, as it produces fewer moles of product compared to \(\mathrm{Ag}_{2} \mathrm{O}\). This is critical because it dictates how much silver sulfadiazine can be formed.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental step in stoichiometry. Molar mass refers to the mass of one mole of a compound, calculated by adding up the atomic masses of each element within the compound's chemical formula. This value is usually expressed in grams per mole \(g/mol\). Knowing the molar mass allows you to convert between mass and moles, a key process in many stoichiometric calculations.To find the molar mass:

• Identify the number of atoms of each element in the compound.
• Look up the atomic mass of each element, typically found on the periodic table.
• Multiply the atomic mass by the number of atoms for each element in the compound and sum up all the products.

For instance, the molar mass of silver sulfadiazine \(\mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{N}_{4} \mathrm{SO}_{2}\) was calculated by adding the atomic masses of all constituent elements, resulting in \(357.144\, g/mol\). This calculation allows us to convert moles of silver sulfadiazine into grams, which is crucial for determining the yield.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be produced from a given amount of reactants, assuming complete conversion with no losses. To calculate this, we need to use the limiting reactant identified in the reaction. Theoretical yield is foundational in determining the efficiency of a chemical process.Steps to calculate theoretical yield include:

• Identify the limiting reactant, which governs the reaction's progress.
• Calculate the moles of product expected, based on the moles of the limiting reactant and the stoichiometry of the reaction.
• Convert these moles into mass using the product's molar mass.

In this exercise, with \(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}\) as the limiting reactant, the theoretical yield of silver sulfadiazine is calculated to be \(35.67\, g\). This assumes a perfect reaction with no side reactions or losses, which gives a baseline for judging actual yields in practical scenarios.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into new substances, called products. Understanding the details of these transformations is essential when predicting the outcomes of reactions, like product formation and quantities.For example, consider the equation:\[ \mathrm{Ag}_2 \mathrm{O}(s) + 2 \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}(s) \longrightarrow 2 \mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{N}_{4} \mathrm{SO}_{2}(s) + \mathrm{H}_2 \mathrm{O}(l) \]This balanced equation shows that \(1\) mole of \(\mathrm{Ag}_2 \mathrm{O}\) reacts with \(2\) moles of \(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}\) to form \(2\) moles of silver sulfadiazine and water. When analyzing chemical reactions:

• The coefficients in the balanced equation indicate the ratio in which reactants combine and products form.
• Using stoichiometry, you can convert between moles of different substances in the reaction.
• Understanding this allows for predicting how much product forms under ideal conditions.

This reaction mechanism is fundamental to stoichiometry, as it sets the stage for calculations regarding limiting reactants, yields, and more.